The Incircle and the Altitudes of a Triangle


	Let ABC be a triangle, AA', BB', and CC' be the altitudes, and the inradius. Then .


	Contributed by: Jay Warendorff

See Theorem 136 in N. Altshiller-Court, College Geometry, Mineola, NY: Dover, 2007 p. 79.

Altitude (Wolfram MathWorld)

Incircle (Wolfram MathWorld)

Inradius (Wolfram MathWorld)

"The Incircle and the Altitudes of a Triangle" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheIncircleAndTheAltitudesOfATriangle/

Contributed by: Jay Warendorff

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Plane Geometry
Triangles

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Altitudes and Incircles
Triangle Altitudes and Inradius
Triangle Altitudes and Circumradius
Area of a Triangle inside the Incircle
A Triangle Inequality Involving the Altitudes, Semiperimeter, Inradius, and Circumradius
The Area of a Triangle inside the Incircle
A Relation between Altitudes of Four Triangles
Six Incircles in an Equilateral Triangle
Dividing a Right Triangle by the Altitude to the Hypotenuse
Area of a Hexagon Formed by the Vertices and Altitude Extensions of a Triangle

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